write a go solution for Description:
Madoka wants to enter to "Novosibirsk State University", but in the entrance exam she came across a very difficult task:

Given an integer n, it is required to calculate sumoperatornamelcm(c,gcd(a,b)), for all triples of positive integers (a,b,c), where a+b+c=n.

In this problem gcd(x,y) denotes the greatest common divisor of x and y, and operatornamelcm(x,y) denotes the least common multiple of x and y.

Solve this problem for Madoka and help her to enter to the best university!

Input Format:
The first and the only line contains a single integer n (3<=n<=10^5).

Output Format:
Print exactly one interger — sumoperatornamelcm(c,gcd(a,b)). Since the answer can be very large, then output it modulo 10^9+7.

Note:
In the first example, there is only one suitable triple (1,1,1). So the answer is operatornamelcm(1,gcd(1,1))=operatornamelcm(1,1)=1.

In the second example, operatornamelcm(1,gcd(3,1))+operatornamelcm(1,gcd(2,2))+operatornamelcm(1,gcd(1,3))+operatornamelcm(2,gcd(2,1))+operatornamelcm(2,gcd(1,2))+operatornamelcm(3,gcd(1,1))=operatornamelcm(1,1)+operatornamelcm(1,2)+operatornamelcm(1,1)+operatornamelcm(2,1)+operatornamelcm(2,1)+operatornamelcm(3,1)=1+2+1+2+2+3=11. Output only the code with no comments, explanation, or additional text.